CN106548137B

CN106548137B - Two degree freedom system Identification of Structural Parameters method based on vibration response signal

Info

Publication number: CN106548137B
Application number: CN201610912276.6A
Authority: CN
Inventors: 姜万录; 朱勇
Original assignee: Yanshan University
Current assignee: Yanshan University
Priority date: 2016-10-20
Filing date: 2016-10-20
Publication date: 2019-03-22
Anticipated expiration: 2036-10-20
Also published as: CN106548137A

Abstract

A kind of two degree freedom system Identification of Structural Parameters method based on vibration response signal, content include: carry out structural excitation, obtain vibration displacement signal；Each rank intrinsic frequency and natural angular frequency of system are obtained using FFT transform；Gained vibration displacement signal is decomposed using Fast Experience mode decomposition method, obtains several intrinsic mode functions (IMF) component；The instantaneous frequency of each IMF component is sought, and is compared with the intrinsic frequency that FFT transform obtains, the IMF component that can represent system frequency is filtered out；The IMF component filtered out is handled using Hilbert transformation, obtain each slow changes amplitude of vibratory response and slow in a disguised form angle and carries out parameters revision；Known parameters are substituted into identification model and solve simultaneously averaged, obtain the structural parameters of system.The present invention can simultaneously using the time-frequency domain information of data, anti-noise ability is strong and can directly utilize vibratory response data progress parameter identification.

Description

Two degree freedom system Identification of Structural Parameters method based on vibration response signal

Technical field

The invention belongs to Identification of Structural Parameters field more particularly to a kind of two degree freedom systems based on vibration response signal Identification of Structural Parameters method.

Background technique

Structural parameters have important influence to system dynamic modeling and vibration control, accurately and effectively identify system Structural parameters have highly important engineering significance.In system vibration is analyzed and controlled, often need to identify its composition knot Physical parameter between the certain components of structure or position.Under normal circumstances, it has been easier to establish the mathematical model of each separate part of system, But then there is larger difficulty for the acquisition of the structural parameters such as the coupling stiffness at interface, damping between each component, and can not be straight Measurement is connect, total system is caused to be difficult to obtain the dynamic analysis result for meeting engineering design needs.In recent years, with number Become vibration engineering circle height using the method for test data identification physical parameter by most attention according to the development of processing technique Spend one of the project of concern.

Traditional parameter identification method is divided into time domain method and frequency domain method, cannot be believed simultaneously using the time domain of data and frequency domain Breath, the precision for causing parameter to identify are restricted.Moreover, traditional parameter identification method must measure pumping signal and sound simultaneously Induction signal, but in practical engineering applications, especially for large scale structure, it is difficult to obtain when there are complex environment excitation Obtain input stimulus.In addition, traditional Modal Parameters Identification is more sensitive to noise, and majority can only handle steady-state signal. Therefore, it needs to invent a kind of time domain that can make full use of data and frequency domain information, anti-noise ability is strong and can directly utilize vibration The new method of dynamic response data progress Identification of Structural Parameters.

Summary of the invention

For above-mentioned there are problem, the present invention provides a kind of two degree freedom system structural parameters based on vibration response signal Discrimination method, it is desirable to provide a kind of time domain that can make full use of data and frequency domain information, anti-noise ability are strong and being capable of direct benefit The new method of Identification of Structural Parameters is carried out with vibratory response data.

The object of the invention is realized by following technical proposals:

Two degree freedom system Identification of Structural Parameters method based on vibration response signal, specific implementation step are as follows:

Step (1): structural excitation is carried out using hammering method, and measures the vibratory response of system using vibrating sensor, is obtained Obtain the vibration displacement signal of each sensor corresponding position；

Step (2): vibration displacement signal obtained by step (1) is calculated using Fourier transformation (FFT), obtains system Each rank intrinsic frequency f of system_iAnd natural angular frequency ω；

Step (3): vibration displacement signal obtained by step (1) is carried out using Fast Experience mode decomposition (FEMD) method It decomposes, obtains several intrinsic mode functions (IMF) component；

Step (4): the phase information φ of each IMF component obtained by Hilbert transform method obtaining step (three) is utilized_j (t), the instantaneous frequency f of each IMF component and then according to expression formula (1) is sought_j(t), the intrinsic frequency of each rank and with FFT transform obtained Rate f_iIt is compared, system frequency (i.e. f can be represented by filtering out_j(t)≈f_i) IMF component；

Step (5): the IMF component that step (4) filters out is handled using Hilbert transform method, is shaken Each slow change amplitude A (t) of dynamic response and slow covert angle φ (t)；

Step (6): are carried out by parameter and is repaired for slow change amplitude and slow covert angle using parameters revision expression formula (2) and formula (3) Just；

A=ω A (t) (2)

Step (7): mass of system m, natural angular frequency ω and revised slow change amplitude a, the slow phase angle theta etc. that becomes are joined Solve in number substitution identification model expression formula (4) and averaged, structural damping c and the structure for obtaining system are rigid Spend k；

X=(C^TC)^-1C^Tb (4)

Wherein:

Beneficial effects of the present invention are as follows:

(1) present invention is different from traditional parameter identification method, can utilize the time domain and frequency of vibratory response data simultaneously Domain information takes full advantage of the effective information of data；

(2) present invention directly can carry out Identification of Structural Parameters using vibration response signal without measuring pumping signal；

(3) it is excellent in terms of handling non-stationary signal to take full advantage of Fast Experience mode decomposition (FEMD) method by the present invention Gesture can resolve into non-stationary, nonlinear properties the data sequence collection of one group of stable state, i.e. intrinsic mode function (IMF) component, lead to The IMF component for representing system frequency can be filtered out by crossing screening rule, to significantly reduce the influence of noise, anti-noise Ability is strong；

Detailed description of the invention

Fig. 1 is the flow chart of the method for the present invention；

Fig. 2 is the two degree freedom system vertical vibration mechanical model of the embodiment of the present invention；

Fig. 3 is the two degree freedom system vertical vibration response of the embodiment of the present invention；

Fig. 4 is the two degree freedom system displacement Signal Amplitude of the embodiment of the present invention；

Fig. 5 is the two degree freedom system displacement signal time-frequency spectrum of the embodiment of the present invention.

Specific embodiment

The present invention will be described in further detail with reference to the accompanying drawings and embodiments.

It is the flow chart of the method for the present invention referring to Fig. 1, specific implementation step is as follows:

A=ω A (t) (2)

X=(C^TC)^-1C^Tb (4)

Wherein:

In order to verify the validity of the method for the present invention, it is vertical to choose two degree freedom system common in the world shown in Fig. 2 Vibration mechanical model is tested, by Newton's second law it is found that its vertical vibration kinetics equation can be by formula (5) and formula (6) It indicates.

In formula, y is upper system with one degree of freedom vibration displacement；Z is lower system with one degree of freedom vibration displacement；F₁For exciting force；m₁、m₂ The equivalent gross mass of respectively upper and lower system with one degree of freedom moving component；c₁、c₂Respectively upper and lower system with one degree of freedom moving component Equivalent damping coefficient；k₁、k₂Equivalent stiffness coefficients between respectively upper and lower system with one degree of freedom moving component and crossbeam；c₁₂For it is upper, Equivalent damping coefficient between lower system with one degree of freedom moving component；k₁₂It is equivalent between upper and lower system with one degree of freedom moving component Stiffness coefficient.

By taking certain two degree freedom system actual structure parameters as an example, numerical experimentation is carried out.Parameter is as follows: m₁=150.9 × 10³kg、m₂=120.7 × 10³Kg, k₁=10.1 × 10¹⁰N/m、c₁=2.6 × 10⁶Ns/m, k₂=6.9 × 10¹⁰N/m、c₂= 1.5×10⁶Ns/m, k₁₂=5.6 × 10¹⁰N/m, c₁₂=5 × 10⁴N·s/m。

It simulates hammering method and carries out structural excitation, exciting force F is applied to upper system with one degree of freedom₁, obtain the vibration displacement of system Signal, as shown in Figure 3.

Vibration displacement signal shown in Fig. 3 is calculated using Fourier transformation (FFT), as a result as shown in Figure 4.By counting Result is calculated it is found that the intrinsic frequency of system is f_i1=126Hz, f_i2=192Hz, corresponding natural angular frequency are ω₁=2 π f_i1= 791.6813rad/s、ω₂=2 π f_i2=1206.3716rad/s.

Vibration displacement signal shown in Fig. 3 is decomposed using FEMD method, obtains several IMF components.

The phase information φ of each IMF component of gained is obtained using Hilbert transform method_j(t), and then according to expression formula (1) the instantaneous frequency f of each IMF component is sought_j(t), as a result as shown in Figure 5.It is computed, gained component after vibration displacement y is decomposed The average instantaneous frequency of IMF1, IMF2 are respectively f_j1=191.5904Hz, f_j2=125.5786Hz；Institute after vibration displacement z is decomposed The average instantaneous frequency for obtaining component IMF1, IMF2 is respectively f_j1=191.9599Hz, f_j2=125.6273Hz.It is obtained with FFT transform To intrinsic frequency be compared it is found that system vibration response decompose after gained component IMF1 average instantaneous frequency f_j1With system Intrinsic frequency f_i2Corresponding (i.e. f_j1≈f_i2), the average instantaneous frequency f of component IMF2_j2With system frequency f_i1It is corresponding (i.e. f_j2≈f_i1), so component IMF1 and IMF2 are the natural mode of vibration components of system.

IMF1 the and IMF2 component filtered out is handled using Hilbert transform method, system with one degree of freedom in acquisition The slow change amplitude A of vibratory response₁(t)、A₂(t) and slow covert angle φ₁(t)、φ₂(t) and lower system with one degree of freedom vibratory response It is slow to become amplitude A₃(t)、A₄(t) and slow covert angle φ₃(t)、φ₄(t)。

Parameters revision is carried out to slow amplitude and the slow covert angle of becoming using parameters revision expression formula (2) and formula (3), then is had: a₁ =ω₁A₁(t), a₂=ω₁A₂(t),a₃=ω₂A₃(t), a₄=ω₂A₄ (t),

By mass of system m₁、m₂, natural angular frequency ω₁、ω₂And revised slow change amplitude a₁、a₂、a₃、a₄, slow covert Angle θ₁、θ₂、θ₃、θ₄Etc. parameters substitute into identification model expression formula (4) and solve and averaged, obtain system Structure d amping coefficient c₁、c₂、c₁₂With rigidity of structure k₁、k₂、k₁₂, the results are shown in Table 1.

The identification result of 1 structural parameters of table

As seen from Table 1, error is smaller between the method for the present invention identification result and true value, available More accurate identification result.

Claims

1. based on the two-degree-of-freedom system structure parameter identification method of vibration response signal, it is characterized in that, the concrete implementation steps of this method are as follows:

Step (1): use the hammering method to excite the structure, and use the vibration sensor to measure the vibration response of the system, and obtain the vibration displacement signal of the corresponding position of each sensor;

Step (2): apply Fourier transform to calculate the vibration displacement signal obtained in step (1), and obtain the natural frequency f _i and natural angular frequency ω of each order of the system;

Step (3): use the fast empirical mode decomposition method to decompose the vibration displacement signal obtained in step (1) to obtain several eigenmode function components;

Step (4): use the Hilbert transform method to obtain the phase information φ _j (t) of each eigenmode function component obtained in step (3), and then obtain the instantaneous frequency of each eigenmode function component according to expression (1) f _j (t), and compare it with the natural frequencies f _i of each order obtained by the Fourier transform, and screen out the eigenmode function components that can represent the natural frequencies of the system, that is, the eigenmode function of f _j (t)≈f _i modal function components;

Step (5): The Hilbert transform method is applied to process the eigenmode function components screened in step (4) to obtain each slowly varying amplitude A(t) and slowly varying phase angle φ(t) of the vibration response;

Step (6): use the parameter correction expressions (2) and (3) to perform parameter correction on the slowly varying amplitude and the slowly varying phase angle;

a=ωA(t) (2)

Step (7): Substitute parameters such as the system mass m, the natural angular frequency ω, the modified slowly varying amplitude a, and the slowly varying phase angle θ into the parameter identification model expression (4) to solve and obtain the average value to obtain the system Structural damping c and structural stiffness k;

X=(C ^T C) ^-1 C ^T b (4)

in: